Toby Driscoll: Software

UD links: UD Math; MATLAB@UD

External links: MATLAB Central; Chebfun

The Schwarz-Christoffel Toolbox for MATLAB

The SC Toolbox is a problem-solving environment for computation and interaction with conformal maps to regions bounded by polygons, including unbounded regions, logical quadrilaterals, and channels. It includes a module for the solution of the Laplace equation on such regions with piecewise constant boundary conditions, to ten digits or more in seconds.

Relevant publications:

T. A. Driscoll. A MATLAB Toolbox for Schwarz-Christoffel mapping. ACM Trans. Math. Soft. 22 (1996), pp. 168-186.
T. A. Driscoll. Algorithm 843: Improvements to the Schwarz-Christoffel Toolbox for MATLAB. ACM Trans. Math. Soft. 31 (2005), 239-251.

The Chebfun system

The Chebfun system is a free MATLAB package hosted ax Oxford University for numerical computation with functions. My interest and contribution to the system is mostly in the chebop class. A chebop is an abstraction of a numerically realized differential or integral operator. Using familiar MATLAB syntax such as \ and eigs, solutions to linear differential boundary value or eigenvalue problems can be obtained with ten or more digits of precision automatically.

Relevant publications:

T. A. Driscoll, F. Bornemann and L. N. Trefethen. The chebop system for automatic solution of differential equations, BIT 48 (2008), 701-723.
T. A. Driscoll. Automatic spectral collocation for integral, integro-differential, and integrally reformulated differential equations. J. Comput. Phys. 229 (2010), 5980--5998.

Other MATLAB software

The function coarserefine.m, as support for this paper on adaptive radial basis function methods. You can find a more advanced variation, for Burgers' equation, at this link.
Some random utilities for MATLAB:

latex		Output a matrix in a format that can be pasted into a LaTeX environment.
gslope		Click on two points and get the slope between them computed automatically.
unplot		Remove the most recently drawn graphics object(s).
wysiwyg		Preview a figure window at the size it will be output in hardcopy.

There are a few others listed in my MATLAB Central area.